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Chapter 3: Problem 17

The Pacific Plate moves north relative to the North American Plate at a rate of \(6 \mathrm{~cm}\) per year. How long will it take Los Angeles (a city on the Pacific Plate) to move northward by \(480 \mathrm{~km},\) the present distance between Los Angeles and San Francisco?

Short Answer

Expert verified
It will take approximately \(8,000,000\) years for Los Angeles to move northward by \(480 \mathrm{~km}\) at a rate of \(6 \mathrm{~cm}\) per year.

Step by step solution

01

Write down the given values and convert them to the same unit

The rate is given in cm/year and the distance is given in km. For consistency, let's convert the distance to centimeters by multiplying by 100,000. Speed (s) = 6 cm/year Distance (d) = 480 km = 480 × 100,000 cm
02

Use the formula: Time = Distance / Speed

To calculate the time (t) it will take for Los Angeles to move, we use the formula: t = d / s Where, - t represents the time it will take for Los Angeles to move. - d is the distance. - s is the speed at which Los Angeles moves.
03

Calculate the time (t)

Now, plug the values of distance and speed into the formula to calculate the time: t = (480 × 100,000 cm) / 6 cm/year t = 48,000,000 cm / 6 cm/year t = 8,000,000 years So it will take approximately 8,000,000 years for Los Angeles to move northward by 480 km (which is the present distance between Los Angeles and San Francisco).

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